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Then the inference is that it would touch both?

It would.

But what do you say to a new point of view? Must not that which is

to touch another be next to that which it is to touch, and occupy

the place nearest to that in which what it touches is situated?


Then the one, if it is to touch itself, ought to be situated next to

itself, and occupy the place next to that in which itself is?

It ought.

And that would require that the one should be two, and be in two

places at once, and this, while it is one, will never happen.


Then the one cannot touch itself any more than it can be two?

It cannot.

Neither can it touch others.

Why not?

The reason is, that whatever is to touch another must be in

separation from, and next to, that which it is to touch, and no

third thing can be between them.


Two things, then, at the least ate necessary to make contact


They are.

And if to the two a third be added in due order, the number of terms

will be three, and the contacts two?


And every additional term makes one additional contact, whence it

follows that the contacts are one less in number than the terms; the

first two terms exceeded the number of contacts by one, and the

whole number of terms exceeds the whole number of contacts by one in

like manner; and for every one which is afterwards added to the number

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